Methods and systems for processing radar signals

A system for detecting objects using a multiple-input multiple-output (MIMO) radar array, comprising:

• a sparse transmitter array of the MIMO radar array comprising a plurality of transmitter antennas, wherein:
• the sparse transmitter array is configured to generate and transmit a radar signal, and
• the radar signal includes mutually orthogonal radar sub-signals that are each generated by one of the plurality of transmitter antennas;
• a sparse receiver array of the MIMO radar array comprising a plurality of receiver antennas, wherein:
• the sparse receiver array is configured to obtain samples of the radar signal, and
• each of the samples of the radar signal is measured by one of the plurality of receiver antennas;
• at least one processor configured to:
• generate a second plurality of samples of the radar signal that each correspond to one of a plurality of available virtual antennas of a virtual array by:
• extracting, from each of the first plurality of samples, sub-samples corresponding to the mutually orthogonal radar sub-signals;
• and
• using the extracted sub-samples to determine a sample of the radar signal for a corresponding available virtual antenna;
• estimate a third plurality of samples of the radar signal that each correspond to one of a plurality of missing virtual antennas of the virtual array by:
• calculating a first spectral density of the radar signal by:
• generating a first phase steering matrix containing phase steering vectors for each of the second plurality of samples, wherein each of the phase steering vectors corresponds to a first frequency of the radar signal and has entries for a first plurality of sub-intervals of an interval of frequencies;
• and
• iteratively calculating a first target backscatter matrix using a first noise matrix, the generated first phase steering matrix, and the second plurality of samples, wherein the first noise matrix represents the interference and noise covariance of the second plurality of samples and is iteratively calculated using the first target backscatter matrix, the generated first phase steering matrix, and the second plurality of samples;
• generating first frequency phase steering vectors for each of the third plurality of samples, wherein each of the first frequency phase steering vectors has entries for the first plurality of sub-intervals of the interval of frequencies;
• calculating entries for each of the first frequency phase steering vectors for the third plurality of samples using the calculated first spectral density of the radar signal;
• extracting a value associated with the first frequency of the radar signal for each of the third plurality of samples from the first frequency phase steering vectors;
• and
• estimate locations of one or more objects by using multi-dimensional folding to process the second plurality of samples and the third plurality of samples by:
• generating a backward matrix and a product of a forward matrix with a target backscatter matrix;
• retrieving parameters of the one or more objects from the backward matrix and the product of the forward matrix with the target backscatter matrix by:
• retrieving values of complex envelopes of the one or more objects using the product of the forward matrix with the target backscatter matrix;
• and
• retrieving values of first frequency components and second frequency components of the one or more objects using the backward matrix;
• and
• calculating the location of the one or more objects using the retrieved parameters.

A non-transitory computer readable medium comprising instructions that, when executed by one or more processors, cause the one or more processors to detect objects using a multiple-input multiple-output (MIMO) radar array by:

• obtaining a first plurality of samples of a radar signal, wherein:
• each of the first plurality of samples of the radar signal is collected by one of a plurality of receiver antennas of a sparse multiple-input and multiple-output (MIMO) receiver array;
• and
• the radar signal comprises a plurality of mutually orthogonal radar sub-signals that are each generated by one of a plurality of transmitter antennas of a sparse MIMO transmitter array;
• generating a second plurality of samples of the radar signal that each correspond to one of a plurality of available virtual antennas of a virtual array by:
• extracting, from each of the first plurality of samples, sub-samples corresponding to the mutually orthogonal radar sub-signals;
• and
• using the extracted sub-samples to determine a sample of the radar signal for a corresponding available virtual antenna;
• estimating a third plurality of samples of the radar signal that each correspond to one of a plurality of missing virtual antennas of the virtual array by:
• calculating a first spectral density of the radar signal by:
• generating a first phase steering matrix containing phase steering vectors for each of the second plurality of samples, wherein each of the phase steering vectors corresponds to a first frequency of the radar signal and has entries for a first plurality of sub-intervals of an interval of frequencies;
• and
• iteratively calculating a first target backscatter matrix using a first noise matrix, the generated first phase steering matrix, and the second plurality of samples, wherein the first noise matrix represents the interference and noise covariance of the second plurality of samples and is iteratively calculated using the first target backscatter matrix, the generated first phase steering matrix, and the second plurality of samples;
• generating first frequency phase steering vectors for each of the third plurality of samples, wherein each of the first frequency phase steering vectors has entries for the first plurality of sub-intervals of the interval of frequencies;
• calculating entries for each of the first frequency phase steering vectors for the third plurality of samples using the calculated first spectral density of the radar signal;
• extracting a value associated with the first frequency of the radar signal for each of the third plurality of samples from the first frequency phase steering vectors;
• and
• estimating locations of one or more objects by using multi-dimensional folding to process the second plurality of samples and the third plurality of samples by:
• generating a backward matrix and a product of a forward matrix with a target backscatter matrix;
• retrieving parameters of the one or more objects from the backward matrix and the product of the forward matrix with the target backscatter matrix by:
• retrieving values of complex envelopes of the one or more objects using the product of the forward matrix with the target backscatter matrix;
• and
• retrieving values of first frequency components and second frequency components of the one or more objects using the backward matrix;
• and
• calculating the location of the one or more objects using the retrieved parameters.

A method for processing radar signals, comprising:

• obtaining a first plurality of samples of a radar signal;
• generating a second plurality of samples of the radar signal that each correspond to one of a plurality of available virtual antennas of a virtual array;
• estimating a third plurality of samples of the radar signal that each correspond to one of a plurality of missing virtual antennas of the virtual array by:
• calculating a first spectral density of the radar signal;
• generating first frequency phase steering vectors for each of the third plurality of samples, wherein each of the first frequency phase steering vectors has entries for a first plurality of sub-intervals of an interval of frequencies calculated using the calculated first spectral density of the radar signal;
• and
• extracting a value associated with the first frequency of the radar signal for each of the third plurality of samples from the first frequency phase steering vectors;
• and
• estimating locations of one or more objects by using multi-dimensional folding to process the second plurality of samples and the third plurality of samples by:
• generating a backward matrix and a product of a forward matrix with a target backscatter matrix;
• retrieving parameters of the one or more objects from the backward matrix and the product of the forward matrix with the target backscatter matrix;
• and
• calculating the location of the one or more objects using the retrieved parameters.